ECAT Pre Engineering Mathematics Test

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

• 7 A
• 8 B
• 9 C
• 10 D

• 
  A
• 
  B
• 
  C
• 
  D

The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is

• 1.2% A
• 1.5% B
• 0.16% C
• 100.16% D

Geometrically the modulus of a complex number represents its distance from the

• Point (1,0) A
• Point (0,1) B
• Point (1,1) C
• Point (0,0) D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

• 4 A
• 5 B
• 2 C
• 3 D

• 
  A
• 
  B
• 
  C
• 
  D

The equation of the circle with centre (h, k) and radius r is

• (x+ h)²+ (y+ k)²= r² A
• (x+ h)²+ (y - k)²= r² B
• (x - h)²+ (y+ k)²= r² C
• (x - h)²+ (y - k)²= r² D

The number of proper subset of A ={a.b.c.d} is

• 3 A
• 6 B
• 8 C
• 15 D

• 
  A
• 
  B
• 
  C
• 
  D

The fifth term of the sequence a_n= 2n + 3 is ______

• 13 A
• -13 B
• 8 C
• 3 D

Projection of vector u along v is

• |v| cosθ A
• |u| cosθ B
• |v| sinθ C
• |u| sinθ D

The number of different ways of describing a set is

• One A
• Two B
• Three C
• Four D

The radius of the circle (x - 1)²+ (y + 3)²= 61 is

• 8 A
• 4 B
• 64 C
• None of these D

A rule that assigns to each elements x in X a unique element y in Y is called a ____________

• domain A
• range B
• function C
• none of these D

For a positive integer n

• n! = n(n + 1) A
• n! = n(n+1)! B
• n! = n(n - 1 ) C
• n! = n(n - 1)! D

If A⊆ B, and B is a finite set, then

• n (a) < n(B) A
• n(B)<(A) B
• n(A)≤ n (B) C
• n(A)≥ n(B) D

• 
  A
• 
  B
• 
  C
• 
  D

If the graph of f is entirely below the x-axis, then the value of definite integral is

• = 0 A
• < 0 B
• > 0 C
• None D

1⁰= ______

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The area of the rhombus whose vertices are A(0,0),B(2,1),C(3,3),D(1,2) is

• 36 square units A
• 3 square units B
• 6 square units C
• 18 square units D

• 
  A
• 
  B
• 
  C
• 
  D

The seventh term of an A.P whose first term is P and common difference is q. is

• P-6q A
• P+6q B
• P-4q C
• P-nq D

The equation of motion of a stone thrown vertically up wards is s = ut - 4.9t²the maximum height attained by it =

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• -1 B
• 1 C
• not defined D

Three consecutive terms of a progression are 30, 24, 20. The next terms of the progression is

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 2 B
• -1 C
• 0 D